The Ulsterman asked the referee if there was a penalty and he was told there was none.
McDowell's pairing with fellow Ulsterman and good friend McIlroy would form one of the most exciting partnerships for Europe.
The Ulsterman has also won in GP2, British Formula 3, British Formula Ford and was a test driver for BAR-Honda.
Playing quickly and happily, in contrast to Woods's brooding Hamlet, the young Ulsterman shoots 63 to tie the course record.
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His team-mate will be fellow Ulsterman Jonathan Rea who missed the second half of the 2004 season because of injury.
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The Ulsterman has been working diligently with the help of a trainer - and with the encouragement of fitness fanatic Woods.
The Ulsterman was part of Ireland's Grand Slam squad, but had to give way to new cap Cian Healy last week.
Open runner-up Thomas Bjorn, Spain's Sergio Garcia, Ulsterman Darren Clarke and Ireland's Paul McGinley also missed the cut on nine over.
It was another polished performance by the Ulsterman, whose kicking out of hand gave his side territorial advantage on numerous occasions.
The Ulsterman won the Scandinavian Masters on only his fourth start as a pro in August and is 54th on the Order of Merit.
Also on Friday, Neil Robertson and Ken Doherty will lock horns for a place in the semi-finals after Australian Robertson beat Ulsterman Joe Swail 4-2.
Ironically, the Ulsterman's only birdie came at the devilishly difficult 18th.
While McIlroy was paired with Matthews and Moul on Tuesday morning there appears little doubt that he will tee up alongside his fellow-Ulsterman Jonathan Caldwell come Saturday.
In other matches, teenage sensation Judd Trump made two century breaks on the way to an impressive 5-2 victory over Ulsterman Joe Swail while Masters champion Mark Selby beat Dave Harold 5-2.
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The Ulsterman, who needs a top three finish at the 'Earth' course in Dubai to stand any chance of overtaking Germany's Kaymer, finished the day well adrift of the leading pack despite moving to two under par after shooting his lowest round of the tournament.
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